Free Logical Problems MCQs with Answers

11. If the price of an item is first increased by 10 per cent and then decreased by 10 per cent, the net effect is

• A. no change
• B. a 1 per cent decrease
• C. a 1 per cent increase
• D. a 10 per cent decrease

Explanation: Starting at 100, a 10 per cent rise gives 110, and a 10 per cent fall on 110 removes 11, leaving 99, so the net change is a loss of 1 per cent. The decrease is larger in absolute terms because it is calculated on a larger base. Successive percentage changes never simply cancel.

12. A sum doubles in 5 years at simple interest. What is the annual rate?

• A. 10 per cent
• B. 15 per cent
• C. 20 per cent
• D. 25 per cent

Explanation: Doubling means the interest earned equals the principal, so 100 per cent is earned over 5 years, which is 20 per cent each year. Under compound interest the same doubling would need a lower rate, since interest earns interest. Simple interest is always calculated on the original principal alone.

13. How many times do the hour and minute hands of a clock overlap in 12 hours?

• A. 10
• B. 11
• C. 12
• D. 13

Explanation: The minute hand gains a full lap on the hour hand 11 times in 12 hours, so they coincide 11 times rather than 12. The overlaps fall roughly every 65 minutes rather than exactly on the hour. Between 11 and 12 o'clock there is no separate overlap, which is where the missing twelfth goes.

14. A box contains 4 red and 6 blue balls. If one ball is drawn at random, what is the probability that it is red?

• A. 0.4
• B. 0.6
• C. 0.25
• D. 0.5

Explanation: There are 4 favourable outcomes out of 10 equally likely ones, so the probability is 4 over 10, that is 0.4. The probability of blue is the complement, 0.6, and the two must add to 1. Checking that the probabilities of all outcomes sum to one is a quick verification.

15. If A can complete a task in 10 days and B in 15 days, how long will they take working together?

• A. 5 days
• B. 6 days
• C. 12.5 days
• D. 25 days

Explanation: In one day A does one tenth and B one fifteenth, and the sum is one sixth, so together they finish in 6 days. The joint time is always shorter than either individual time, which rules out the last two options at once. Adding rates rather than times is the key step.

16. A father is three times as old as his son. Five years ago he was four times as old. What is the son's present age?

• A. 10 years
• B. 15 years
• C. 20 years
• D. 12 years

Explanation: Let the son be x and the father 3x, so five years ago 3x minus 5 equals four times x minus 5, giving 3x minus 5 equals 4x minus 20 and x equal to 15. Checking, the father is now 45, and five years ago he was 40 against the son's 10, which is four times. Age problems are almost always solved with one variable and one equation.

17. The ratio of boys to girls in a class is 3 to 2. If there are 30 boys, how many students are there in total?

• A. 45
• B. 50
• C. 40
• D. 60

Explanation: Three parts correspond to 30 boys, so one part is 10 and the two parts of girls are 20, giving 50 students in total. Answering 45 comes from adding the wrong number of parts. Finding the value of a single part first is the reliable route through any ratio question.

18. A student scores 60, 70 and 80 in three tests. What must be scored in a fourth test to average 75?

• A. 85
• B. 90
• C. 95
• D. 80

Explanation: An average of 75 over four tests needs a total of 300, and the first three sum to 210, so the fourth must be 90. Working from the required total rather than adjusting the average directly is the safer method. The answer exceeds 75 because the earlier scores pulled the average down.

19. If 15 April falls on a Monday, what day is 1 May of the same year?

• A. Monday
• B. Tuesday
• C. Wednesday
• D. Thursday

Explanation: April has 30 days, so 1 May is 16 days after 15 April, and 16 divided by 7 leaves a remainder of 2, moving the day forward from Monday to Wednesday. Counting the exact gap in days before taking the remainder is essential. Errors usually come from miscounting the length of the month.

20. A car travels 60 km at 30 km per hour and returns the same distance at 60 km per hour. Its average speed for the whole journey is

• A. 45 km per hour
• B. 40 km per hour
• C. 50 km per hour
• D. 35 km per hour

Explanation: The outward leg takes 2 hours and the return 1 hour, so the total is 120 km in 3 hours, giving 40 km per hour. Averaging the two speeds to get 45 is wrong because more time is spent at the slower speed. Average speed is always total distance divided by total time.